help fill out the proof

Answer:
Step V: Transitive property of Inequality
Step VI: Subtraction Property of Inequality
Step-by-step explanation:
In Step IV, the RHS of t=both the sides are equal.
So, they equated the LHS of both the sides.
This is the transitive property of equality which states that if a = b and c = b then a = c.
In this case, a = [tex]$ \angle {m_1} + \angle {m_2} $[/tex]
b = 180⁰
c = [tex]$ \angle {m_2} + \angle {m_3} $[/tex]
Consequently, [tex]$ \angle {m_1} + \angle {m_2} = \angle {m_2} + \angle {m_3} $[/tex]
In step VI, [tex]$ \angle {m_2} $[/tex] is subtracted on both the sides. So, this is called as Subtraction Property of Equality.